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Datasets:
SAIRfoundation
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equational-theories-selected-problems

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id
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26
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eq1_id
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End of preview. Expand in Data Studio

Equational Theories Selected Problems

Update (April 27, 2026)

This dataset was updated on April 27, 2026.

Main changes:

  • added the released Stage 1 final evaluation subsets: evaluation_normal, evaluation_hard, evaluation_extra_hard, and evaluation_order5
  • added metadata files for the new evaluation subsets
  • updated the README and metadata to reflect the current released subsets

Update (March 24, 2026)

This dataset was updated on March 24, 2026.

Main changes:

  • added eq1_id and eq2_id to all released subsets
  • added the hard3 subset
  • updated the README to reflect the current released subsets

This dataset contains selected problem subsets for the Mathematics Distillation Challenge: Equational Theories, including public training subsets and released Stage 1 evaluation subsets.

This dataset is intended for Stage 1 of the Mathematics Distillation Challenge: Equational Theories competition.

Competition page:

The full raw implication dataset contains 4694 laws, which yields 4694 * (4694 - 1) = 22,028,942 ordered implications.

The full raw implications table can be downloaded from the Equational Theories Project implications page by selecting Download raw implications table:

The full list of all 4694 equations is available here:

Because the full raw dataset is very large, the competition organizers selected public subsets to make testing and experimentation more practical for participants.

Subsets

  • normal: 1000 selected problems, chosen programmatically, with 500 ground-truth TRUE labels and 500 ground-truth FALSE labels
  • hard: 200 selected problems co-curated by human mathematicians and AI, with 74 ground-truth TRUE labels and 126 ground-truth FALSE labels
  • hard1: a deduplicated version of the 200-problem hard subset, containing 69 unique problems total, with 24 ground-truth TRUE labels and 45 ground-truth FALSE labels
  • hard2: 200 selected problems co-curated by human mathematicians and AI, with 100 ground-truth TRUE labels and 100 ground-truth FALSE labels
  • hard3: 400 selected problems with 195 ground-truth TRUE labels and 205 ground-truth FALSE labels
  • evaluation_normal: 200 Stage 1 final evaluation problems, with 100 ground-truth TRUE labels and 100 ground-truth FALSE labels
  • evaluation_hard: 200 Stage 1 final evaluation problems, with 100 ground-truth TRUE labels and 100 ground-truth FALSE labels
  • evaluation_extra_hard: 200 Stage 1 final evaluation problems, with 100 ground-truth TRUE labels and 100 ground-truth FALSE labels
  • evaluation_order5: 200 order-5 evaluation problems, with 100 ground-truth TRUE labels and 100 ground-truth FALSE labels

All subsets are exposed as the train split in this repository. The evaluation_* subsets are released Stage 1 evaluation subsets.

Data Schema

Each record has the following fields:

  • id: stable identifier such as normal_0001, hard_0001, hard3_0001, or evaluation_normal_0001
  • index: 1-based index within the subset
  • difficulty: subset difficulty label such as normal, hard, extra_hard, or order5_normal
  • eq1_id: 1-based equation identifier for equation1; for the order-4-and-below subsets, this refers to the full 4694-law equation list
  • eq2_id: 1-based equation identifier for equation2; for the order-4-and-below subsets, this refers to the full 4694-law equation list
  • equation1: Equation 1
  • equation2: Equation 2
  • answer: whether Equation 1 implies Equation 2 over all magmas

Subset Metadata

Subset-level metadata for the official released subsets is stored under metadata/.

Each metadata file contains:

  • subset_name: subset identifier
  • source: release source, such as official
  • curators: list of named curators, if provided
  • difficulty: subset difficulty label
  • problem_count: total number of problems in the subset
  • true_count: number of ground-truth TRUE labels
  • false_count: number of ground-truth FALSE labels
  • selection_method: high-level selection method such as programmatic, human, or human_ai
  • derived_from: parent subset name if the subset is derived from another subset
  • notes: optional explanatory notes

Records in hard1, hard2, and hard3 use subset-specific IDs and keep difficulty: hard. Records in evaluation_order5 use order-5 equation identifiers.

Usage 

from datasets import load_dataset

normal = load_dataset(
    "SAIRfoundation/equational-theories-selected-problems",
    "normal",
    split="train",
)

hard = load_dataset(
    "SAIRfoundation/equational-theories-selected-problems",
    "hard",
    split="train",
)

hard1 = load_dataset(
    "SAIRfoundation/equational-theories-selected-problems",
    "hard1",
    split="train",
)

hard2 = load_dataset(
    "SAIRfoundation/equational-theories-selected-problems",
    "hard2",
    split="train",
)

hard3 = load_dataset(
    "SAIRfoundation/equational-theories-selected-problems",
    "hard3",
    split="train",
)

evaluation_normal = load_dataset(
    "SAIRfoundation/equational-theories-selected-problems",
    "evaluation_normal",
    split="train",
)

evaluation_hard = load_dataset(
    "SAIRfoundation/equational-theories-selected-problems",
    "evaluation_hard",
    split="train",
)

evaluation_extra_hard = load_dataset(
    "SAIRfoundation/equational-theories-selected-problems",
    "evaluation_extra_hard",
    split="train",
)

evaluation_order5 = load_dataset(
    "SAIRfoundation/equational-theories-selected-problems",
    "evaluation_order5",
    split="train",
)

Files

  • data/normal.jsonl
  • data/hard.jsonl
  • data/hard1.jsonl
  • data/hard2.jsonl
  • data/hard3.jsonl
  • data/evaluation_normal.jsonl
  • data/evaluation_hard.jsonl
  • data/evaluation_extra_hard.jsonl
  • data/evaluation_order5.jsonl
  • metadata/normal.json
  • metadata/hard.json
  • metadata/hard1.json
  • metadata/hard2.json
  • metadata/hard3.json
  • metadata/evaluation_normal.json
  • metadata/evaluation_hard.json
  • metadata/evaluation_extra_hard.json
  • metadata/evaluation_order5.json
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